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What Special About This Number
red for the properties in dozenal (dependent in which base is used, in this wiki, we always use the dozenal base). 0 is the additive identity. 1 is the multiplicative identity. 2 is conjectured to be the only cyclic number that does not divide any Carmichael number. 3 is the smallest k'' such that it is impossible to construction of an angle equal to 1/''k of a given arbitrary angle using only an unmarked straightedge and a compass. 4 is the smallest number of colors sufficient to color all planar maps. 5 is the smallest k'' such that general algebraic equation with degree ''k cannot be solved algebraically. 6 is the smallest possible order of nonabelian group. 7 is the smallest k'' such that regular ''k-gon is not constructible using a compass and an unmarked straightedge. 8 is the smallest positive integer with no primitive roots. 9 is the only number k'' such that (''k times a triangular number) plus 1 (i.e. centered k''-gonal number) is always also a triangular number. X is the smallest noncototient number. E is the largest squarefree number ''n such that the quadratic field OQ(√−n) is a Euclidean domain. 10 appears in the value of the Riemann zeta function at −1 (i.e. ζ(−1) = −1/10). 11 is the number of Archimedean solids. 12 is the smallest nontotient number. 13 is the smallest k''>1 such that the number of terms of the ''k-th cyclotomic polynomial does not equal to the largest prime factor of k''. 14 is the only number of the form ''ab'' = ''ba'', with ''a, b'' nonnegative integers, ''a ≠ b''. 15 is the only positive Genocchi prime. 16 is the smallest proven solitary number which is not coprime to its sum-of-divisors. 17 is the smallest number (and the only number ≤50) not appearing in the first 100 terms of Recamán's sequence (in fact, 17 does not appear in the first 49800 terms of Recamán's sequence, the first time 17 appearing is term 49872, if 0 is term 0, 1 is term 1). 18 is the number of moves (quarter or half turns) required to optimally solve a Rubik's Cube in the worst case. 19 is the smallest number of distinct squares needed to tile a square. 1X is the numerator of an approximation of π (1X/7). 1E is the smallest number ''n such that the relative class number h- of cyclotomic field Q(e''2πi/''n) is greater than 1. 20 is the largest number for which the Dirichlet characters are all real. 21 is the smallest square that can be written as a sum of 2 positive squares. 22 is the only positive number to be directly between a square and a cube. 23 is the number n'' for which (the largest number in the 3''x+1 sequence starting at n'')/(''n''2) is largest. (i.e. 5414/(23^2) = 10.7E7314) 24 is the smallest even number which is a (Fermat) pseudoprime to some nontrivial bases. 25 is the largest number ''n such that 2''x''2 + n'' is prime for all 0≤''x≤''n''−1. (since it is divisible by n'' for ''x = n'', one cannot do be better than this) 26 is the largest number with the property that all smaller numbers relatively prime to it are prime or 1. 27 is one of the only two numbers which is a repunit in three or more bases (not including base 1). 28 is the smallest number ''n such that the n''-th row of the modulo-2 Pascal's triangle (the top row, which contains only one 1, is the 0th row, not the 1st row), when read in binary, is not a number of the sides of constructible regular polygon. 29 is the largest number that is not a sum of distinct triangular numbers. 2X is the smallest number with the property that it and its neighbors have the same number of divisors. 2E is the smallest possible order of magic square with consecutive primes starting with 3. 30 is the smallest perfect power which is not a prime power. 31 is the smallest irregular prime. 32 is the magic constant of the only non-trivial normal magic hexagon. 33 is the smallest ''n which is not power of 10 such that n''.''n.n''...''n.n''.1 (dot means concatenation) cannot be prime. 34 is the smallest ''n such that n''.111...111 (dot means concatenation) cannot be prime. 35 is the largest number ''n such that x''2 + ''x + n'' is prime for all 0≤''x≤''n''−2. (since it is divisible by n'' for ''x = n''−1, one cannot do be better than this) 36 is the largest number of sides of a regular polygon that can fill a point with other regular polygons. 37 is the smallest number ''n such that (define a(n): a(0)=a(1)=1; thereafter a(n+1) = sum(a(k)^2,k=0..n)/n) a(n) is not integer. 38 is the smallest n'' such that all of ''n.0, n''.1, ''n.2, ..., n''.E (dot means concatenation) are composite. (i.e. all of 10''n+0, 10''n''+1, 10''n''+2, ..., 10''n''+E are composite) 39 is the smallest odd positive integer that is not power of squarefree number. 3X is the largest even number which is a value of D'' for incrementally largest values of minimal ''x satisfying Pell equation x^2−Dy^2=1. 3E is the smallest base for which no generalized Wieferich primes are known. 40 is the largest number n'' such that the sum of the first ''n positive triangular numbers is also a triangular number. 41 is the smallest number with the property that it and its neighbors are not squarefree. 42 is the smallest number which can be written as the sum of of 2 positive squares in 2 different ways. 43 is the number of groups with order 25 (=28). 44 is the smallest untouchable number > 5 (the conjectured only odd untouchable number). 45 is the smallest prime that produces prime reciprocal magic square. 46 is the smallest totient number which is not totient of squarefree number. 47 is the largest triangular number in the Fibonacci sequence. 48 is the only number n such that no x^2 mod n is prime and n is not Euler's "numerus idoneus" (or convenient numbers, or idoneal numbers). 49 is the smallest number >1 of the form Φ''n''(2) which is neither prime nor Fermat pseudoprime base 2. 4X is the largest squarefree even number n'' such that the imaginary quadratic field Q(√−n) has class number 2. 4E is the smallest prime factor of the smallest composite Euclid number (i.e. 4E|(11#+1) = 15467 = 4E×365). 50 is the smallest order of nonsolvable group. 51 is conjectured to be the largest number ''n such that kn−1 and kn+1 are not both primes for all k'' ≤ 4''n. 52 is the smallest number that can be written as the sum of of 3 distinct squares in 2 ways. 53 is the largest number of the form a''n'' − b''n'' with no primitive prime factors (26 − 16). 54 is the smallest number >1 which is both square number and cube number. 55 is the smallest deceptive prime. 56 is the denominator of the first Bernoulli number whose absolute value is not a unit fraction (B''X = 5/56). 57 is the smallest prime which is both Bernoulli irregular and Euler irregular. 58 is the smallest ''n which is not power of 10 and not congruent to 1 mod 11 (in which all such numbers are divisible by 11) such that (n''k''.1) (dot means concatenation) is composite for all 1≤''k''≤1000. (the smallest k''≥1 such that this number is prime is 2781E5) 59 is the largest minimal primitive root in the primes ≤100000 (for the prime 54201). (Note that for the primes <54201, the largest minimal primitive root is 38 (for the prime 35641), which is less than 59×(2/3) or 59×80%) 5X is the smallest weird number. 5E is the largest number whose square is one more than a factorial number. 60 is the smallest Achilles number. 61 is the largest squarefree number ''n such that the quadratic field OQ(√n) is a Euclidean domain. 62 is the number of different non-Hamiltonian polyhedra with a minimum number of vertices. 63 is the number of uniform polyhedra, excluding the infinite sets. 64 is the smallest n'' such that ''n-Fibonacci numbers cannot be primes. 65 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1. 66 is the dimension of the exceptional Lie group E''6. 67 is the smallest prime number ''p for which the real quadratic field Q√p has class number greater than 1. 68 is conjectured to be the largest possible number of consecutive integers n'' such that the quadratic polynomial ''an''2 + ''bn + c'' are primes (in the case ''n''2 + ''n + 35, which is prime for all −34≤''n''≤33, but not for n''=−35 or ''n = 34). 69 is the only known square n'' such that ''n×2''n''−1 is prime (Woodall prime). 6X is the number of 6-hexes. 6E is the smallest odd prime p'' (let a(''p) is the smallest generalized Wieferich prime base p'') such that a(a(''p)) = p''. 70 is the smallest number ''n such that n'' is neither squarefree nor of the form ''pa''q'b'' with p'', ''q primes, but no simple group with order n'' exists. 71 is the largest number ''n such that the sum of the first n'' positive square numbers is a triangular number. 72 has a 4th root that starts 3.0662666762266... (there are 8 6's in the first 11 digits after the dozenal point) 73 is the sum of the squares of the first four primes. 74 is the smallest abundant number coprime to the smallest odd abundant number (669). 75 is the smallest prime to start a Cunningham chain of the first kind of ≥6 terms. (note that 2 starts a Cunningham chain of the first kind of 5 terms) 76 is the smallest pronic number which is nontotient. (note that pronic number n×(n−1) cannot be nontotient if p is prime, since this number equals φ(p2) 77 is the smallest positive integer expressible as a sum of two cubes in two different ways if negative roots are allowed. 78 is the largest possible number of faces of an Archimedean solid. 79 is the smallest number ''n such that the distance from n'' to closest prime is >3. 7X is the smallest number ''n>1 such that M''(''n) is positive, where M'' is the Mertens function. 7E is the third-smallest number whose aliquot sequence terminates at 6 (within the sequence {7E, 21, 6}). 80 is the only number ''n besides 2 with the property that not n'' but ''n/2 is a value of k'' for incrementally largest values of groups of order ''k sets a record. 81 is the smallest base not of the form n''2''k+1 or of the form 4''n''4 (where generalized Wagstaff numbers can be factored algebraically) for which no generalized Wagstaff (probable) primes are known. 82 is the only known number n'' of the form 2''p''2 with odd prime ''p such that Φ''n''(2) is (probable) prime. 83 is the smallest number whose factorial is greater than googol (=10100). 84 is the smallest number with more than one factorization into L''-primes. (Let ''L = {1, 4, 7, X, 11, 14, 17, 1X, ..., 3''k''+1, ...}; then an L''-prime is in ''L but is not divisible by any members of L'' except itself and 1. 85 is the alternating factorial of 5. 86 is the smallest number ''n for which (let n'' = 2a0 × 3a1 × 5a2 × 7a3 × Ea4 × ...) a0 + a1''x + a2''x''2 + a3''x''3 + ... = 0 does not have algebraic solution (i.e. there is no solution in radicals). 87 is the smallest Lucas-Wieferich prime associated with the pair (P'', ''Q) = (4, 1). 88 is the smallest number of unit line segments that can exist in a plane with four of them touching at every vertex. 89 is the smallest integer such that the factorization of ''x'n''−1 over Q'' includes coefficients other than ±1. In other words, the 89th cyclotomic polynomial, Φ89, is the first with coefficients other than ±1. 8X is the denominator of an approximation of π (239/8X). 8E is the smallest prime ''p ends with E such that 2''p''−1 is prime. 90 is the number of heptominoes (7-minoes). 91 is the number of different families of subsets of a three-element set whose union includes all three elements. 92 is the smallest number n'' such that there are no known powerful number ''k such that k''+''n is also powerful. 93 is the magic constant of the smallest magic square using only 1 and prime numbers. 94 is the side of the smallest square that can be tiled with distinct integer-sided squares. 95 is the denominator of an approximation of π (257/95). 96 is the starting number of the first run of 11 consecutive composite numbers. 97 is the number of rooted trees with 8 vertices. 98 is the number of irreducible polynomials of degree 6 over a 3-element field. 99 is the smallest possible length of the longest side of a Heronian tetrahedron (one whose sides are all rational numbers). 9X is the smallest n'' such that the range ''n, n'' + 1, ... 4''n/3 contains at least one prime from each of these forms: 4''k'' + 1, 4''k'' - 1, 6''k'' + 1 and 6''k'' - 1. 9E is the largest number n'' such that the ''n''th triangular number is also a tetrahedral number. X0 is the smallest number to appear 6 times in Pascal's triangle. X1 is the only Brazilian number with exactly 3 divisors. X2 is the number of partitions of 20 into distinct parts. X3 is the smallest ''k for which there is no known prime of the form (k''−1)×''kn''+1. X4 is the smallest nontotient which is also an untouchable number. X5 is the largest two-digit narcissistic number. X6 is the number of different semigroups on 4 elements (up to isomorphism and reversal). X7 is the smallest de Polignac number. X8 is the largest number that is not a sum of distinct square numbers. X9 is the smallest number that can be written as the sum of 3 squares in 4 ways. XX is the only integer that is the sum of the squares of its first four divisors. XE is the smallest Sophie Germain prime congruent to 3 mod 4 which is not safe prime. E0 is the smallest non-squarefree Catalan number. E1 is the smallest overpseudoprime base 10. E2 is the smallest number whose aliquot sum is a weird number. E3 is the product of the first two odd composite numbers. E4 is the only number which is a self-descriptive number in some base (base 4) which has a smaller self-descriptive number (84). E5 is the smallest strictly non-palindromic number ''n>4 such that n''+2 is also strictly non-palindromic. E6 is the smallest number whose aliquot sequence has length >20 (in fact, >120, its length is 12X). E7 is the smallest number ''n such that there are no known (probable) primes of the form (n''+1)''k − n''k''. E8 is the largest number whose square is a tetrahedral number. E9 is the smallest n''>1 such that ''n×2''n''+1 is prime (Cullen prime). EX is the number of planar graphs with 6 unlabeled vertices. EE is the only product of twin primes which is not brilliant number. 100 is the largest square number in the Fibonacci sequence. 101 is the smallest base for which no generalized Woodall primes are known. 102 is the smallest number which is nontotient, noncototient, and untouchable. 103 is the number of sided 6-hexes. 105 is the smallest number which is not sum of two prime powers (including 1). 108 was once the smallest base not of the form n^x (where generalized repunits can be factored algebraically) for which no generalized repunit (probable) primes are known (currently, the smallest such base is 135). 109 is the sum of the first 5 positive factorials. 110 is the smallest number that is the product of two different substrings. 111 is the smallest irregular prime with irregular index greater than 1. 114 is the smallest number n'' with exactly 10 solutions to the equation φ(''x) = n''. 115 is the smallest Harshad number >10 divisible by neither E nor 10. 116 is the smallest number >100 with terminate reciprocal. 117 is the largest Heegner Number. 11E is a permutable prime. 120 is the smallest order of noncyclic simple group other than groups of the form ''Ak'' (which is always a noncyclic simple group for ''k≥5). 121 is the largest square number in the Pell sequence. 125 is the smallest 3-digit Keith number. 129 is the magic constant of the smallest magic square using only prime numbers. 12E is the smallest nonpalindromic number whose square is palindromic. 130 is the largest possible number of edges of an Archimedean solid. 131 is the largest value x'' satisfying the Ramanujan–Nagell equation. 133 is the largest number that equal the sum of the squares of the digits of their own square. 135 is the smallest composite primeval number. 141 is the largest number that can be written as ''ab + ac + bc with 0 < a'' < ''b < c'' in a unique way. 143 is the smallest ''n such that binomial(2''n'', n'') is divisible by ''n''2. 145 is the smallest prime ''p such that none of 2''p''+1, 4''p''+1, 8''p''+1, X''p''+1, 12''p''+1, and 14''p''+1 is prime. (Sophie Germain proved that Fermat's last theorem is true for all odd primes p'' such that at least one of 2''p+1, 4''p''+1, 8''p''+1, X''p''+1, 12''p''+1, and 14''p''+1 is prime) 147 is the largest k'' such that all positive values of ''k−2''n''2 are primes or 1. 148 is the largest number n'' ≤ 100000000 such that |''M(n'')| ≥ (√''n)/2, where M'' is the Mertens function. (Mertens conjectured that |''M(n'')| < √''n for all n'' > 1, this is now known to be false) 151 is the smallest odd number ''D with no prime factors p'' = 3 mod 4 but the period of continued fractions of √''n is even. 155 is the smallest even base for which no generalized Cullen primes or generalized Woodall primes are known. 156 is the largest number n'' such that all primes between ''n/2 and n'' yield a representation as a sum of two primes. 160 is conjectured to be the only number not of the form ''t+''p'', with t'' triangular number (including 0 and 1), ''p either prime or 0. 163 is the number of space groups, not including handedness. 164 is the smallest member of amicable pairs. 172 is the number of space groups, including handedness. 173 is the smallest number with ≥3 odd prime factors whose cyclotomic polynomial has all coefficients ±1. 174 is the number of digits of 100!. 175 has a palindromic reciprocal: 0.0074EE470074EE4700... 179 is conjectured to be the smallest Lychael number. 17E is the largest number that cannot be written as a sum of 8 or fewer cubes. 180 is the kissing number in 8 dimensions. (note that the true value of the kissing number is only known in 1, 2, 3, 4, 8, and 20 dimensions) 181 is the smallest (and the only known) 3-Wall-Sun-Sun prime. 182 is the smallest n'' such that ''n, n''+1, ''n+2, and n''+3 have the same number of divisors. 183 is the smallest Frugal number. 187 is the largest proper divisor of the smallest Hardy-Ramanujan number (1001). 191 is the smallest non-trivial triangular star number. 193 is the smallest perfect totient number to be neither a power of three nor thrice a prime. 194 is the value of 24 (where ''nm'' is the tetration). 195 is the only known Fermat prime which is irregular prime. 19E is the smallest prime ''p such that (p''−1)/2 is irregular prime. 1X3 is the number of groups with order 26 (=54). 1X5 is the smallest prime base for which no generalized repunit (probable) primes are known. 1X7 is the smallest prime ''p such that neither p''−1 nor ''p+1 is cubefree. 1E1 is the 8th Euler (or up/down) number. 1E4 is the base with the largest conjectured smallest generalized Sierpinski number and the largest conjectured smallest generalized Riesel number in all bases ≤1000. 1E7 is the smallest n'' such that φ7(''n) > 1. 1E8 is the smallest n'' appearing twice in ''P union Q'' union ''R defined with: Construct sequences P'', ''Q, R'' by the rules: ''Q = first differences of P'', ''R = second differences of P'', ''P starts with 1, 3, 9, Q'' starts with 2, 6, ''R starts with 4; at each stage the smallest number not yet present in P'', ''Q, R'' is appended to ''R. 1E0 is the smallest number whose aliquot sequence has not yet been fully determined. 1EX is the smallest nonsemiprime which is a possible value of the smallest (Fermat) prime base n''. 200 is the smallest ''n>8 such that both n'' and ''n+1 are powerful. 202 is the smallest n'' such that a positive definite integral quadratic form is universal if it takes the numbers from 1 to ''n as values. (a more precise version states that, if an integer valued integral quadratic form represents all the numbers 1, 2, 3, 5, 6, 7, X, 11, 12, 13, 15, 17, 19, 1X, 1E, 22, 25, 26, 27, 2X, 2E, 31, 36, 4X, 79, 92, 101, 14E, 202, then it represents all positive integers) 210 is the smallest nonsquare number which is not a primitive root mod any safe prime. 221 is the number of intersections when all the diagonals of a regular dozagon are drawn. 222 is the smallest happy number which is not power of 10. 223 is the smallest odd number n'' such that φ(''n) < φ(n''−1). 225 is the smallest number ''n such that kn+1 is not prime for all k''≤20. 22E is the smallest composite ''n such that F''n''−(5|''n'') = 0 mod n'', where ''Fn'' is the ''n''th Fibonacci number, and (''m|''n'') is the Jacobi symbol. 245 is the smallest (Fermat) pseudoprime base 2 (Sarrus number). 255 is the smallest number whose 4th power can be written as the sum of four 4th powers. 262 is the smallest even base for which no generalized Carol primes are known. 265 is the smallest number that can be written as a sum of consecutive squares in more than 1 way. 269 is the number of octominoes (8-minoes). 274 is the smallest generalized Riesel number base 10. 275 is the largest Fibonacci number n'' such that the period length of 1/''n is ≤10. 276 is the smallest n'' ≠ X mod E for which there are no non-titanic prime of the form ''n×10''k''+1. 278 is the smallest even base not of the form n^x (where generalized repunits can be factored algebraically) for which no generalized repunit (probable) primes are known. 280 is the order of the hyperoctahedral group for n'' = 4. 281 is the smallest integer such that the factorization of ''xn''−1 over ''Q includes coefficients other than ±1 and ±2. 293 is the smallest Lucas-Carmichael number. 298 is the n'' for which the smallest prime of the form ''n×10''k''+1 is largest for all n'' < 375 (the smallest generalized Sierpinski number base 10). 2X1 is conjectured to be the largest prime ''p whose smallest primitive root is larger than √''p''. 2XX is the smallest non-primepower k'' such that binomial(2''k, k'') = 2 (mod ''k). (besides, 2XX is also the only known such even k'') 2EE is the smallest prime ''p>E ends with E'' such that the period length of 1/''p is not (p''−1)/2. 309 is the smallest number with more than one factorization into ''S-primes. (Let S'' = {1, 5, 9, 11, 15, 19, ..., 4''k+1, ...}; then an S''-prime is in ''S but is not divisible by any members of S'' except itself and 1. 318 is the largest number that cannot be written as a sum of 7 or fewer cubes. 326 is conjectured to be the largest base ''b for which there are no (Fermat) pseudoprimes ≤''b''+1. 330 is the largest module for the known property of odd perfect numbers. (the known property of odd perfect numbers is = 1 mod 10, or = 99 mod 330, or = 69 mod 230) 340 is the largest number n'' such that carmichael_lambda(''n) = 8. 344 is the smallest square number which is nontotient. 34E is the smallest irregular prime with irregular index greater than 2. 350 is the smallest number of faces such that holyhedron is known to exist. 353 is the largest sum-product number. 354 is the third perfect number. 360 is the largest number n'' such that carmichael_lambda(''n) = 6. 368 is the only known cube n'' such that ''n×2''n''−1 is prime (Woodall prime). 369 is the smallest nonsquare automorphic number. 375 is the square root of the smallest Perrin pseudoprime. 378 is the starting number of the first run of 15 consecutive composite numbers. 380 is the smallest number which can not be made prime by changing one of its digits. 388 is the smallest number > e''2π. 3X8 is the smallest number which is a Rhonda number in some base (base 10). 3X9 is the smallest Carmichael number. 3XX is the smallest number not itself an amicable pair which terminates at an amicable pair. 3XE is the largest known Wilson prime. 3E8 is conjectured to be the largest base ''b for which there are no (Fermat) pseudoprimes ≤''b''−1. 404 is the smallest number n'' such that φ(''x) = n'' has only two solutions and the smaller of this two solutions is not prime power (including 1). 420 is the largest possible number of cells of 4-dimention polytope. (note that for ''n-dimention polytope, n''≥5, the only possible number of cells are ''n+1, 2''n'', and 2''n'') 42E is the smallest number whose square is an even-digit palindromic number. 455 is the smallest prime which is a prime factor of a composite Fermat number. 470 is the smallest n'' (and the only ''n≤1000) such that k''×''n is Harshad number for all k''≤600000. (the smallest ''k such that 470''k'' is not Harshad number is 750275) 497 is the first irregular prime to appear in the numerator of a Bernoulli number. 4X5 is the length of a repunit prime. 4X9 is the smallest composite n'' such that ''Ln'' = 1 mod ''n, where L''n'' is the n''th Lucas number. 4E6 is conjectured to be the largest number ''n such that n''×(''n+1) is a primorial (15#). 520 is the constant term of modular function j as power series in q=e^(2\pi i t). 598 is the smallest weird number which also an untouchable number. 5X0 is the largest number n'' such that ''k^2 mod n'' is square number for all ''k coprime to n. 5E6 is the Kaprekar constant for 3-digit numbers. 620 is the starting number of the first run of 17 consecutive composite numbers. 666 is the "beast number". 668 is the smallest 3-digit narcissistic number. 669 is the smallest odd abundant number. 66X is conjectured to be the largest even number which is (Fermat) pseudoprime to 1/4 of the bases coprime to it. 704 is conjectured to be the largest base b'' for which there are no (Fermat) pseudoprimes <''b−1. 771 is the smallest Wieferich prime. 77E is the number of steps for the Conway's game of Life starting with the "F-pentomino" to stabilize. 780 appears in the aliquot sequence of 780/4 (=1E0), which is the smallest number whose aliquot sequence has not yet been fully determined. 781 is the smallest deceptive prime which is not semiprime. 782 is the smallest number n'' which is (Fermat) pseudoprime to exactly 11 bases 0≤''b≤''n''−1. (note that for all 1≤''k''≤11, but not for k''=12, there exists number ''n which is (Fermat) pseudoprime to exactly k'' bases 0≤''b≤''n''−1, and for k''=11, the smallest such number ''n is largest for all these values of k'') 7X2 is the starting number of the first run of 19 consecutive composite numbers. 8X4 is the smallest ''n>7 such that n''! is not Harshad number. 8X7 is an exponent of Mersenne primes. 928 is the starting number of the first run of 29 consecutive composite numbers. (no other such number <5640) X83 is the only 3-digit narcissistic number with distinct digits. X91 is the smallest number not the sum of a perfect power (including 1, but not including 0) and a prime (there are only two known such numbers, the other is E6). E60 is the smallest even base for which no generalized Carol primes or generalized Kynea primes are known. EE6 is conjectured to be the largest number ''n which is not quadratic residue mod all primes p''≤√''n not dividing n''. For 1001 1001 is the smallest number which can be written as the sum of of 2 positive cubes in 2 different ways. 1001 is the smallest 4-digit palindromic number. 1001 is the smallest absolute Euler pseudoprime. 1001 is the smallest palindromic number which cannot be prime when read in any base. 1001 is the smallest Carmichael number of the form (6''n+1)×(10''n''+1)×(16''n''+1) with all 6''n''+1, 10''n'+1, and 16''n''+1 primes.'' Sequence of uninteresting numbers Numbers that are not (primes, E-smooth, perfect powers, or palindromes): 2X, 32, 3X, 43, 49, 4X, 52, 58, 59, 62, 64, 6X, 71, 72, 73, 78, 79, 7X, 7E, 86, 8X, 93, 96, 97, 98, 9X, 9E, X2, X3, X4, X9, E1, E2, E4, E6, E9, EX, 102, 104, 108, 109, 10E, 110, 112, 113, 115, 118, 11X, 122, 123, 124, 126, 129, 12X, 132, 133, 134, 135, 136, 137, 138, 13X, 142, 143, 149, 14X, 14E, 150, 152, 153, 154, 155, 158, 159, 15X, 15E, 162, 163, 165, 166, 16X, 170, 172, 174, 176, 177, 178, 179, 17X, 184, 186, 187, 188, 189, 192, 193, 196, 197, 198, 199, 19X, 1X2, 1X3, 1X4, 1X8, 1X9, 1XX, 1E0, 1E2, 1E3, 1E6, 1E8, 1E9, 1EX, 1EE, 203, 204, 207, 208, 20X, 20E, 211, 213, 214, 215, 216, 219, 21X, 220, 224, 226, 227, 229, 22X, 22E, 231, 233, 234, 235, 238, 239, 23X, 23E, 243, 244, 245, 246, 248, 249, 24X, 250, 253, 256, 257, 258, 259, 25X, 264, 265, 266, 268, 269, 26X, 26E, 270, 274, 275, 278, 279, 27X, 283, 284, 286, 287, 289, 28X, 28E, 293, 296, 297, 298, 29X, 29E, 2X0, 2X3, 2X4, 2X5, 2X6, 2X7, 2X8, 2X9, 2XX, 2E3, 2E4, 2E5, 2E6, 2E7, 2E8, 2E9, 2EX, 302, 304, 305, 306, 30X, 310, 311, 312, 317, 318, 319, 31X, 31E, 320, 322, 324, 328, 329, 32X, 330, 331, 332, 334, 335, 336, 337, 338, 339, 33X, 341, 342, 345, 348, 349, 350, 351, 352, 354, 355, 356, 359, 35X, 361, 362, 364, 366, 367, 369, 36X, 36E, 370, 371, 372, 374, 376, 378, 37X, 37E, 382, 384, 385, 386, 387, 388, 389, 38X, 392, 394, 395, 396, 398, 399, 39E, 3X0, 3X1, 3X2, 3X4, 3X6, 3X7, 3X9, 3XX, 3E0, 3E1, 3E2, 3E4, 3E6, 3E8, 3E9, 3EX, 3EE, 402, 403, 405, 406, 407, 408, 409, 40X, 411, 412, 413, 417, 418, 419, 41X, 422, 423, 426, 428, 429, 42X, 42E, 430, 432, 433, 436, 438, 439, 43X, 43E, 440, 442, 443, 445, 448, 449, 44X, 44E, 450, 451, 452, 453, 456, 458, 459, 45X, 461, 462, 463, 466, 467, 468, 469, 46X, 472, 473, 475, 476, 477, 478, 479, 47X, 47E, 482, 486, 487, 488, 489, 48X, 490, 491, 493, 495, 496, 498, 49X, 49E, 4X0, 4X1, 4X2, 4X3, 4X6, 4X7, 4X9, 4XX, 4XE, 4E0, 4E2, 4E3, 4E5, 4E6, 4E7, 4E8, 4E9, 4EX, 501, 502, 503, 504, 508, 50X, 50E, 510, 512, 514, 516, 518, 519, 51X, 520, 521, 522, 523, 524, 528, 529, 52X, 52E, 532, 533, 534, 536, 537, 538, 539, 53X, 53E, 543, 544, 546, 547, 548, 549, 54X, 54E, 550, 551, 552, 553, 556, 558, 559, 55X, 55E, 561, 562, 563, 564, 566, 567, 569, 56X, 56E, 570, 571, 572, 573, 574, 578, 579, 57X, 57E, 580, 581, 582, 583, 584, 586, 588, 58X, 590, 592, 593, 594, 596, 597, 598, 599, 59X, 5X2, 5X3, 5X4, 5X6, 5X8, 5X9, 5XX, 5XE, 5E0, 5E2, 5E3, 5E4, 5E6, 5E8, 5E9, 5EX, 601, 602, 603, 604, 605, 607, 608, 609, 60X, 610, 612, 613, 618, 619, 61X, 620, 621, 622, 624, 625, 627, 629, 62X, 62E, 631, 632, 633, 634, 635, 638, 639, 63X, 640, 641, 642, 643, 644, 645, 648, 649, 64X, 64E, 651, 652, 653, 654, 657, 658, 659, 65X, 65E, 660, 662, 663, 664, 667, 668, 66X, 670, 671, 672, 673, 674, 677, 678, 679, 67X, 67E, 682, 683, 684, 685, 689, 68X, 691, 692, 693, 694, 697, 699, 69X, 6X0, 6X1, 6X2, 6X3, 6X4, 6X5, 6X8, 6X9, 6XX, 6XE, 6E0, 6E2, 6E3, 6E5, 6E7, 6E8, 6E9, 6EX, 6EE, 702, 703, 704, 706, 708, 709, 70X, 710, 712, 713, 715, 716, 718, 71X, 720, 722, 723, 724, 725, 726, 728, 729, 72X, 72E, 730, 731, 732, 733, 734, 738, 739, 73X, 73E, 741, 742, 743, 744, 746, 748, 749, 74X, 74E, 750, 752, 753, 754, 755, 756, 758, 759, 75E, 761, 762, 763, 764, 765, 766, 768, 76X, 770, 772, 773, 774, 776, 779, 77X, 780, 781, 782, 783, 784, 786, 788, 789, 78X, 78E, 790, 792, 793, 795, 796, 798, 79X, 79E, 7X0, 7X2, 7X3, 7X4, 7X5, 7X8, 7X9, 7XX, 7XE, 7E0, 7E1, 7E2, 7E3, 7E4, 7E5, 7E6, 7E8, 7E9, 7EX, 802, 805, 806, 807, 809, 80X, 810, 811, 812, 813, 814, 815, 816, 819, 81X, 81E, 821, 822, 823, 824, 826, 827, 829, 82X, 831, 832, 833, 834, 836, 837, 839, 83X, 83E, 842, 843, 844, 845, 846, 847, 849, 84E, 850, 852, 854, 856, 857, 859, 85X, 860, 862, 863, 864, 866, 869, 86X, 86E, 870, 872, 873, 874, 875, 876, 877, 879, 87X, 87E, 880, 883, 884, 885, 886, 887, 889, 88X, 891, 892, 893, 894, 895, 896, 897, 899, 89X, 89E, 8X0, 8X1, 8X2, 8X3, 8X4, 8X6, 8X9, 8XX, 8E0, 8E1, 8E2, 8E3, 8E4, 8E6, 8E9, 8EX, 8EE, 902, 903, 904, 906, 908, 90X, 910, 911, 912, 913, 914, 915, 916, 917, 918, 91X, 922, 924, 925, 926, 928, 92X, 930, 931, 932, 933, 934, 935, 936, 937, 938, 93X, 93E, 941, 942, 943, 944, 945, 947, 948, 94X, 94E, 950, 951, 952, 953, 954, 956, 957, 958, 95X, 960, 962, 963, 966, 968, 96X, 96E, 970, 972, 973, 974, 975, 977, 978, 97X, 97E, 980, 981, 982, 983, 984, 985, 986, 98X, 98E, 990, 991, 992, 993, 996, 997, 998, 99X, 99E, 9X0, 9X1, 9X2, 9X3, 9X4, 9X5, 9X6, 9X8, 9XX, 9E0, 9E2, 9E3, 9E4, 9E6, 9E7, 9E8, 9EX, X01, X02, X03, X05, X06, X08, X09, X12, X13, X14, X15, X18, X19, X1E, X20, X21, X22, X23, X24, X25, X28, X29, X2E, X30, X31, X32, X33, X34, X36, X38, X40, X42, X43, X44, X46, X47, X48, X49, X51, X52, X53, X54, X55, X56, X57, X58, X59, X61, X62, X63, X64, X65, X66, X67, X68, X70, X71, X72, X73, X74, X75, X76, X78, X79, X7E, X81, X82, X83, X85, X86, X88, X89, X8E, X90, X92, X93, X94, X96, X97, X98, X99, XX0, XX1, XX2, XX3, XX4, XX5, XX6, XX9, XE0, XE1, XE2, XE4, XE5, XE6, XE8, XE9, E01, E02, E03, E04, E05, E06, E07, E08, E09, E0X, E10, E12, E13, E16, E17, E18, E19, E1X, E20, E22, E23, E24, E26, E27, E28, E2X, E32, E33, E34, E35, E36, E38, E39, E3X, E40, E41, E42, E43, E44, E46, E47, E48, E49, E4X, E50, E51, E52, E53, E54, E55, E57, E58, E59, E5X, E60, E62, E63, E64, E65, E66, E68, E69, E6X, E70, E72, E73, E74, E75, E76, E77, E78, E79, E7X, E82, E83, E84, E85, E86, E87, E88, E89, E8X, E90, E93, E94, E96, E98, E9X, EX0, EX1, EX2, EX3, EX4, EX6, EX7, EX8, EX9, EXX, EE0, EE1, EE2, EE3, EE4, EE6, EE8, EE9, EEX, ... 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